Finite Group Databasebeta

← #38767991

Subgroups — #38767991

Order 25472.

206 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#27164748C211yesmaximal, characteristic
2#27164397C211yesmaximal, characteristic
3#27164314C212yesmaximal
4#27163748C212yesmaximal
5#333×C199C211yesmaximal, characteristic
6C2×#15691876—22no—
7#20263955C2211yescharacteristic
8#20263954—22no—
9#20263953—22no—
10C4×Dic398C2212yes—
11#20263920—22no—
12#20263889—22no—
13#20263880—22no—
14C4×C199⋊C8C2211yescharacteristic
15C4⋊Q8×C199C2211yescharacteristic
16C4⋊C8×C199C2212yes—
17C2×Dic398—22no—
18C2×Dic398—21no—
19C2×Dic398D412yes—
20#15691876—44no—
21C2×C199⋊C8—21no—
22C4⋊Dic199—22no—
23C4⋊Dic199D412yes—
24Dic199⋊C4—24no—
25Dic199⋊C4—22no—
26C4×Dic199—22no—
27C4×Dic199—22no—
28C2×Q8×C199D412yes—
29C2×C8×C199—22no—
30C4⋊C4×C199—22no—
31C42×C199C2311yescharacteristic
32Dic398—22no—
33Dic398—42no—
34Dic398—82no—
35Dic398Q1614yescomplemented
36C2×Dic199—22no—
37C2×Dic199—22no—
38C2×Dic199—41no—
39C199⋊C8—22no—
40Q8×C199—42no—
41C2×C4×C199—22no—
42C2×C4×C199C2×D412yes—
43C2×C4×C199C2×D411yescharacteristic
44C8×C199—42no—
45C22×C199#12011yescharacteristic
46C4×C199—21no—
47C4×C199—42no—
48C4×C199C2×Q1612yes—
49C4×C199#13712yes—
50Dic199—24no—
51Dic199—42no—
52Dic199—81no—
53C2×C199#45112yes—
54C2×C199#45311yescharacteristic
55C199#163311yescharacteristic, complemented, Sylow
56#1633—1991nomaximal, Sylow
57Q82—1991no—
58#494—1991no—
59#477—1992no—
60#333D19911yescharacteristic
61Q8⋊C8—1992no—
62C2×Q16—3982no—
63C4⋊Q8—3982no—
64C4⋊Q8—3982no—
65C4⋊Q8—1991no—
66C4⋊Q8C2×D19911yescharacteristic
67C4×Q8—3982no—
68C4×Q8—1992no—
69#107—3982no—
70C4⋊C8C2×D19912yes—
71#103—3982no—
72C4×C8—1991no—
73C2×Q8—3982no—
74C2×Q8—3981no—
75C2×Q8—1992no—
76C2×Q8D79612yes—
77Q16—7964no—
78C2×C8—22no—
79C2×C8—3981no—
80C4⋊C4—22no—
81C4⋊C4—3984no—
82C4⋊C4—3982no—
83C4⋊C4—3982no—
84C4⋊C4—1992no—
85C42—3982no—
86C42—3982no—
87C42C22×D19911yescharacteristic
88Q8—42no—
89Q8—7962no—
90Q8—15922no—
91Q8—3982no—
92Q8—1994no—
93C2×C4—22no—
94C2×C4—7961no—
95C2×C4—3982no—
96C2×C4—3982no—
97C2×C4D4×D19912yes—
98C2×C4C2×D79611yescharacteristic
99C8—42no—
100C8—3982no—
101C22#2026392511yescharacteristic
102C4—21no—
103C4—42no—
104C4—7962no—
105C4—15921no—
106C4—3984no—
107C4Q16×D19912yes—
108C4#2026398412yes—
109C2#2716417512yes—
110C2#2716418811yescharacteristic
subgroupG/H
centerC22#20263925
commutator, cosocleC42×C199C23
FrattiniC42C22×D199
Fitting#333×C199C2
socle, prime radicalC22×C199#120
hypercenter#333D199
hypocenterC199#1633
LCSG ▷ C42×C199 ▷ C22×C199 ▷ C199
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
35. Dic398Q16semidirect
55. C199#1633semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#271647482
#271643972
#271643142
#271637482
#333×C1992
#1633199